Assignment-1 - MECH646 Wheeled Mobile Robots Danielle Sami...

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MECH646 Wheeled Mobile Robots Danielle Sami Nasrallah Department of Mechanical Engineering Faculty of Engineering and Architecture American University of Beirut 2010-10-28
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ASSIGNMENT 1 Exercise 1: Falling rolling disk In this exercise we consider a falling rolling disk, which corresponds, of course, to a more realistic case than the example studied in class. Figure 1: Falling Rolling Disk 1. Define the vector q of generalized coordinates 2. Compute the angular velocity of the falling rolling disk 3. Compute the velocity of the centre of the disk under the pure-rolling assumption 4. Derive the kinematic constraints 5. Write the kinematic constraints in the Pfaffian form 6. Apply the Frobenius theorem to show the nonholonomy of the falling rolling disk
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Exercise 2: Omnidirectional symmetric three-wheeled mobile robot The robot has three Omni-directional wheels located at three non-consecutive sides of a regular hexagon, as illustrated in Fig.2. Contrary to conventional wheels, where under pure-
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